8 Feb 2016
School
Department
Course
Professor
MAT136Lecture12TrigonometricIntegrals
Sine/Cosine
inxdxosx
∫
s= − c+c
osxdxsinx
∫
c= + c
Example1
inxdxinx inxdx
∫
s5=∫
s4•s
u=cosx,du=sinxdx(sinx) inxdx=∫
2 2 •s
(1 osx) sinxdx=∫
−c2 2
− (1 ) (du)= ∫
−u2 2
−u du=∫
1 − 2 2+u4
u= ( − 3
2u3+ )
5
u5
+c
osx=c−3
2cosx
3+5
cosx
5+c
Ex2
osxdx osxcosxdx
∫
c3=∫
c2
u=sinx,du=cosxdx(1 inx)cosxdx=∫
−s2
(1 )du=∫
−u2
=u−3
u3+c
inx=s−3
sinx
3+c
Ex3